Diketahui (1)/(A)+(1)/(B)=(1)/(20),

A = 30

Pembahasan

Diketahui:
(1)/(A) + (1)/(B) = (1)/(20)  ...(1)
(1)/(B) + (1)/(C) = (1)/(12)  ...(2)
(1)/(A) + (1)/(C) = (1)/(10)  ...(3)

Untuk mencari nilai A, kita bisa menjumlahkan ketiga persamaan tersebut:
[(1)/(A) + (1)/(B)] + [(1)/(B) + (1)/(C)] + [(1)/(A) + (1)/(C)] = (1)/(20) + (1)/(12) + (1)/(10)
2(1)/(A) + 2(1)/(B) + 2(1)/(C) = (3 + 5 + 6)/(60)
2[(1)/(A) + (1)/(B) + (1)/(C)] = (14)/(60)
2[(1)/(A) + (1)/(B) + (1)/(C)] = (7)/(30)
(1)/(A) + (1)/(B) + (1)/(C) = (7)/(60)  ...(4)

Sekarang, kita bisa mencari nilai (1)/(A) dengan mengurangkan persamaan (2) dari persamaan (4):
[(1)/(A) + (1)/(B) + (1)/(C)] - [(1)/(B) + (1)/(C)] = (7)/(60) - (1)/(12)
(1)/(A) = (7)/(60) - (5)/(60)
(1)/(A) = (2)/(60)
(1)/(A) = (1)/(30)

Maka, nilai A adalah 30.